Two cylinders \(A\) and \(B\) of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. \(B\) is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is: 
1. adiabatic 
2. isochoric 
3. isobaric 
4. isothermal 

The \((P\text{-}V)\) diagram for an ideal gas in a piston-cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is:

Thermodynamic processes are indicated in the following diagram: 
   
Match the following: 

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then,

A monoatomic gas at a pressure \(P\), having a volume \(V\), expands isothermally to a volume \(2V\) and then adiabatically to a volume \(16V\). The final pressure of the gas is: \(\left(\text{Take:}~ \gamma = \frac{5}{3} \right)\)

One mole of an ideal gas goes from an initial state \(A\) to the final state \(B\) with two processes. It first undergoes isothermal expansion from volume \(V\) to \(3V\) and then its volume is reduced from \(3V\) to \(V\) at constant pressure. The correct \((P-V)\) diagram representing the two processes is:

1.		2.
3.		4.